Neural Koopman Lyapunov Control
release_2occi2ozxjh3nbwqtmv2otrzae
by
Vrushabh Zinage, Efstathios Bakolas
2022
Abstract
Learning and synthesizing stabilizing controllers for unknown nonlinear
control systems is a challenging problem for real-world and industrial
applications. Koopman operator theory allows one to analyze nonlinear systems
through the lens of linear systems and nonlinear control systems through the
lens of bilinear control systems. The key idea of these methods lies in the
transformation of the coordinates of the nonlinear system into the Koopman
observables, which are coordinates that allow the representation of the
original system (control system) as a higher dimensional linear (bilinear
control) system. However, for nonlinear control systems, the bilinear control
model obtained by applying Koopman operator based learning methods is not
necessarily stabilizable. Simultaneous identification of stabilizable lifted
bilinear control systems as well as the associated Koopman observables is still
an open problem. In this paper, we propose a framework to construct these
stabilizable bilinear models and identify its associated observables from data
by simultaneously learning a bilinear Koopman embedding for the underlying
unknown control affine nonlinear system as well as a Control Lyapunov Function
(CLF) for the Koopman based bilinear model using a learner and falsifier. Our
proposed approach thereby provides provable guarantees of asymptotic stability
for the Koopman based representation of the unknown control affine nonlinear
control system as a bilinear system. Numerical simulations are provided to
validate the efficacy of our proposed class of stabilizing feedback controllers
for unknown control-affine nonlinear systems.
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